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  "body": "\n## Summary\n\nThe sinc function is $\\operatorname{sinc} x = \\frac{\\sin x}{x}$, with the value $1$ at $x = 0$.\nSignal processing often uses the normalised version $\\frac{\\sin \\pi x}{\\pi x}$, whose zeros are the non-zero integers.\nThe normalised sinc function is the [[Fourier transform|DPVM34ADZV]] of the indicator function of an interval, and it is the interpolation kernel in the sampling theorem.\nIts integral over $(0, \\infty)$ is the [[Dirichlet integral|0GZNSHMG4Q]], equal to $\\frac{\\pi}{2}$.\n\n## Explanations\n\n### L1 human\n\nThe sine wave $\\sin x$ goes up and down forever with the same height.\nDividing by $x$ makes the waves smaller and smaller far from the origin.\nNear $0$ both $\\sin x$ and $x$ are small, and their quotient is close to $1$.\nSo the graph has a tall central hump of height $1$ and decaying ripples on both sides, crossing zero at $\\pm\\pi, \\pm 2\\pi, \\ldots$.\n",
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